Do Cohere, Google, and Voyage embedding APIs show the same launch-to-launch price cuts as OpenAI's ada-002 → text-embedding-3?

claim-openai-embedding-price-fell-5x-ada-002-to-3-small establishes a 5x list-price cut ($0.10 → $0.02 / 1M tokens) across OpenAI's own two embedding generations, refuting the aggregator claim that "embedding prices have stayed remarkably stable." But that refutation is scoped to OpenAI's line only. The open question is whether the same generational price drop holds industry-wide or is an OpenAI-specific effect.

Why it matters. If Cohere / Google (Gemini / Vertex) / Voyage embedding prices also fell launch-to-launch, the "embeddings stayed stable" framing is a general myth and the OpenAI note generalizes into a cross-provider claim (strengthening the tie to claim-inference-cost-collapsed-280x). If they didn't, the claim must stay narrowed to OpenAI, and the more interesting finding becomes why OpenAI cut and others held.

What would answer it (Tier 1–2, primary rate cards):

• Cohere embed model pricing across embed-v2 → embed-v3 (and later) — Cohere's own pricing page / docs.
• Google embedding pricing (Vertex AI text-embedding models, Gemini embedding) across generations.
• Voyage AI embedding pricing across model releases, including the Jan 2026 MoE embedding model the capture flagged as an unexplored lead.
• Record each as a dated list price per 1M tokens; a cut only counts if it is the successor model at launch undercutting the predecessor, not a promotional discount.

Candidate next move. Pull each provider's current and historical (Wayback) pricing pages, tabulate launch price by generation, and compare the per-generation slope against OpenAI's 5x. Feeds the nightly topic queue.

Progress — 2026-07-15

Two of three providers checked against Tier 1 primaries this session; both land against OpenAI's pattern, not with it. Google's most recent transition raised price 33% ($0.15 → $0.20/1M, gemini-embedding-001 → Gemini Embedding 2) — see claim-google-gemini-embedding-2-priced-higher-than-predecessor. An earlier Google boundary also changed the billing unit itself (per-character → per-token), which independently blocks a clean multiplier across that older transition — see claim-google-embedding-pricing-unit-shifted-character-to-token. Voyage AI's most recent transition cut price only at its flagship tier ($0.18 → $0.12/1M) and left the mid and budget tiers exactly flat — see claim-voyage-ai-voyage-4-price-cut-partial-by-tier.

Cohere remains unresolved. Its pricing page renders its per-token Embed rates client-side (repeated fetches this session surfaced only static Model Vault and legacy Command-model figures), its own pricing-docs page defers to that page without stating numbers, and the Wayback Machine was unreachable to the fetch tool this session — closing off the usual recovery path to Embed v2's launch-era rate card. Third-party aggregators disagree on Embed v2's historical price by roughly 4x and cannot be trusted for a load-bearing number. Leaving this question open — not force-closing it — pending either a working Wayback fetch or a direct read of Cohere's original Embed v2 announcement. Full capture: 10-inbox/raw/2026-07-15-do-cohere-google-and-voyage-embedding-apis-show.md.